Further pure math 2 (Edexcel AS and A level Modular Mathemaics)

Inequalities

Solving inequalities by manipulation

Solving inequalities graphically

Series

Using the method of differences to sum simple finite series

Further complex numbers

The modulus–argument form

Euler’s relation

Multiplying and dividing two complex numbers

De Moivre’s theorem

De Moivre’s theorem applied to trigonometric identities

Using de Moivre’s theorem to find the nth roots of a complex number

Using complex numbers to represent a locus of points on an Argand diagram

Using complex numbers to represent regions on an Argand diagram

Applying transformations that map points on the z-plane to points on the w-plane by applying a formula relating z = x + iy to w = u + iv

Review Exercise 1

First order differential equations

Solving first order differential equations with separable variables and the formation of differential equations and sketching members of the family of solution curves

Solving exact equations where one side is the exact derivative of a product and the other side can be integrated with respect to x

Solving first order linear differential equations of the type dy/dx + Py = Q by multiplying through the equation by an integrating factor to produce an exact equation

Using a given substitution to reduce a differential equation into one of the above types of equation, which you can then solve

Second order differential equations

Finding the general solution of the linear second order differential equation a d²y/dx² + b dy/dx + cy = 0, where a, b and c are constants and where b² > 4ac

Finding the general solution of the linear second order differential equation a d²y/dx² + b dy/dx + cy = 0, where a, b and c are constants and where b² = 4ac

Finding the general solution of the linear second order differential equation a d²y/dx² + b dy/dx + cy = 0, where a, b and c are constants and where b² < 4ac

Finding the general solution of the linear second order differential equation a d²y/dx² + b dy/dx + cy = f(x), where a, b and c are constants, by using y = complementary function + particular integral

Using boundary conditions to find a specific solution of the linear second order differential equation, or initial conditions to find a specific solution

Using a given substitution to transform a second order differential equation into one of the above types of equation, and solving it

Maclaurin and Taylor series

Finding and using higher derivatives of functions

Expressing functions of x as an infinite series in ascending powers of x using Maclaurin’s expansion

Finding the series expansions of composite functions using known Maclaurin’s expansions

Finding an approximation to a function of x close to x = a, where a ≠ 0, using Taylor’s expansion of the function

Finding the solution, in the form of a series, to a differential equation using the Taylor series method

Polar coordinates

Polar and Cartesian coordinates

Polar and Cartesian equations of curves

Sketching polar equations

Areas using polar coordinates

Finding tangents parallel and perpendicular to the initial line

Review Exercise 2

Examination style paper

Answers

Index